You've had so much good advice here, it's hard to add much more. As everyone has said, much larger, much more often temperature and pH matched water changes are the best medicine most of the time.
You do however have

and what has happened here is that the new fish have brought in something that was symptomless at the time of purchase and presented with symptoms one week later. This is why QTing new fish must be between
3 and 4 weeksminimum to allow for the surfacing of symptoms that can then be treated appropriately before adding to the main tank. New fish are 90% of the time carrying a whole wagonload of baddies. Some even say the conditions at the store will guarantee parasites are on board every new fish - period. This is why all new fish should be treated with salt (kills many parasites) and prazi (in PC tabs- for flukes; the most common parasite perhaps & the one that salt won't work on).
But you know all that now!
Fins this red are symptomatic of
a combination of troubles ranging from stress, high nitrates, ammonia/nitrite and then also parasites and bacterial sepsis.
I think your fish are suffering from all of these.So, what I would begin with is (and while you are looking for a larger tank or rubbermaid to house half of your fish)
1) salting. Start with one teaspoon of the right kind of salt for each US gallon of water in the tank. Click on the link in my sig on how to salt.
2) Then have a look at your local store and see if you can find some
parasite clear tank buddy tabs. These are a combination medication useful for new fish and contain the essential prazi and also some metrodizanole which is an anti-inflammatory antibiotic that should help for the sepsis.
You do need to medicate in perfect water. You are doing very well so far and I'm sure you can manage it well. PC tabs are added every 3 days I believe, check instructions and salting must be done slowly over 3 days after a very large water change. After 3 days and when the salt is up to 0.3% you need to do a 50% water change
daily adding back 0.15% (that is half) of the total salt. Your fish have been flashing, are very stressed, are all bottom sitting and have severe fin sepsis and really do need these 2 meds.
Think of it as a belated QT for the new fish, but it is for all the fish now. Hope you can get started soon